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Business Spreadsheets

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1) Calculate X-Bar-Bar, R-Bar, and associated control limits using the data in the table above.
From the data we have, the X-Bar-Bar number can be seen at the top set of results titled Centre x-bar bar = 5.1 a. The R-Bar result is the “Center” result the bottom set of data is R-Bar. Therefore R-Bar = 1.083 2) Create X-Bar•R (Average & Range) Control Charts from the data in the table above.

The X-Bar Control Chart is shown below

Control limits for the x - chart are: Control limits = x- bar ± A2 (MR) Control limits = 5.1 ± 0.729 *1.083 Control limits = 4.31 to 5.89 Control limits ranges between 4.31 to 5.89

The R Control Chart is shown below

Control limits for R- chart are: Upper control limits = (MR) * D4 Upper control limits = 2.282 *1.083 Upper control limits = 2.47

Lower control limit = D3 * MR Lower control limit = 0 * 1.083 Lower control limit = 0

3) Discuss notable out-of-control conditions displayed in the completed X-Bar•R (Average & Range) Control Charts.

We consider points outside the control limits. We do not consider runs, set of points within certain regions. From the X-Bar control chart, we can see that two points 19 and 21 are above the upper control limit. From the R-Chart we can see that one point, 18 is above the upper control limit.

4. If the conditions you note could be defined as assignable conditions and they are removed from the process, what will happen to the X-Bar•R Control Chart?
The new table formed after removing the three points, with sample size 27 is shown below

Sample | 1 | 2 | 3 | 4 | | 1 | 4.92 | 4.26 | 4.94 | 4.29 | 2 | 4.65 | 5.54 | 5 | 5.42 | 3 | 5.77 | 5.26 | 4.76 | 4.79 | 4 | 6.25 | 4.88 |

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